I How do we know that both plates of a capacitor have the same charge?

[Kashmir]

Suppose we have two conductors ( can be of different shapes) and connect them to battery.
Why would equal amounts of charge appear on the two conductors?

 

[Ibix]

What was the initial net charge in the system? Can charge be created or destroyed?

 

[PeroK]

Suppose we have two conductors ( can be of different shapes) and connect them to battery.
Why would equal amounts of charge appear on the two conductors?

Do you have a particular set-up in mind? In general, if the total charge on a system is zero, then the positively charged components must have equal and opposite charge in total to the negatively charged components.

 

[Kashmir]

What was the initial net charge in the system? Can charge be created or destroyed?

Maybe the two plates of capacitor have unequal charges. The excess goes to battery somehow.

 

[Kashmir]

Do you have a particular set-up in mind? In general, if the total charge on a system is zero, then the positively charged components must have equal and opposite charge in total to the negatively charged components.

Yes that should be true for the whole system. Battery, wires and plates of capacitor.

Charge conservation doesn't necessarily imply equal amounts of charges on the two plates of capacitor.

 

[PeroK]

Yes that should be true for the whole system. Battery, wires and plates of capacitor.

Charge conservation doesn't necessarily imply equal amounts of charges on the two plates of capacitor.

IMO, you asked the wrong question. Your question should have been: how does a battery work?

In fact, Heisenberg nearly failed his PhD examination because he didn't know how a storage battery worked!

 

[PeroK]

https://www.wired.com/2015/02/battery-doesnt-store-charge-work/

 

[kered rettop]

They don't have to be precisely equal. However if they are not, that means there is an overall charge. In electrical terms, that overall charge is on the self-capacitance of the capacitor. Let's put some numbers on it.
Take a 100uF capacitor. Place 1,000 microcoulombs on one plate and -1,000 on the other. The capacitor is then charged to 10v and there is no left-over charge. But now add a further charge of 1 nanocoulomb to one plate. That's one part in a million imbalance. A typical small capacitor might have a self-capacitance of 1 pF. The nanocoulomb raises its potential by 1000 volts - 100 times the plate-to-plate voltage.
You also have what are usually called "stray" capacitances, such as from the body of the capacitor to adjacent conductors, be they "earth/ground" or something else. These may very well be a bit larger than the self capacitance but if we say 10pF, that still leaves the one part per million imbalance raising the overall potential by 100 volts.

So there is no absolute law saying the charges are the same. However if they are not, there will be huge voltages trying to get the imbalance away. Besides which, you are most unlikely to want to operate a capacitor like that.

No, you can't just get rid of a charge "into the battery". Sometimes garage mechanics don't use scientific terms very accurately. To a mechanic, putting charge into a battery means sending a current through it. So the charge that goes in is equal to the charge that comes out. A battery doesn't just magically absorb charge.

 

[kered rettop]

https://www.wired.com/2015/02/battery-doesnt-store-charge-work/

Well, it does and it doesn't. Shove an amp-hour through the battery and you will later be able to get nearly an amp-hour back. That's charge storage. Not quite the same as sticking "pure charge" into a storage bottle, of course.